Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Show that 32x−1=9x33^{2x - 1} = \frac{9^x}{3}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Composition of linear and quadratic functions: find a valueright chevron icon

Full solution

Q. Show that 32x−1=9x33^{2x - 1} = \frac{9^x}{3}
  1. Simplify Right Side: Let's start by simplifying the right side of the equation, (9x)/3(9^x)/3. We know that 99 is 323^2, so we can rewrite 9x9^x as (32)x(3^2)^x.
  2. Apply Exponent Property: Now, using the property of exponents that (ab)c=ab∗c(a^b)^c = a^{b*c}, we can simplify (32)x(3^2)^x to 32∗x3^{2*x}. So, 9x3\frac{9^x}{3} becomes 32∗x3\frac{3^{2*x}}{3}.
  3. Use Exponent Rule: Next, we can use the property of exponents that am/an=am−na^{m}/a^{n} = a^{m-n} to simplify 32∗x/33^{2*x}/3. Since 33 is the same as 313^1, we can write 32∗x/33^{2*x}/3 as 32∗x−13^{2*x - 1}.
  4. Finalize Equation: Now we have 32x−13^{2x - 1} on both sides of the equation.\newlineThis means that 32x−13^{2x - 1} is indeed equal to (9x)/3(9^x)/3.

More problems from Composition of linear and quadratic functions: find a value

Question
Find the inverse of the function. y=x+3 y = x + 3 Write your answer in the form ax+b ax + b . Simplify any fractions. y= y = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find (r∘s)(x)(r \circ s)(x).\newliner(x) = 33x\newlines(x) = 22x + 55\newlineWrite your answer as a polynomial in simplest form.\newline(r∘s)(x)=(r \circ s)(x) = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
What is (f+g)(x)(f + g)(x)?\newlinef(x)=−3xf(x) = -3x\newlineg(x)=3x+1g(x) = 3x + 1\newline\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline‾\underline{\hspace{3cm}}\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x+4f(x) = -x + 4\newlineg(x)=4xg(x) = 4x\newline\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline‾\underline{\hspace{3em}}\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the domain of (fg)(x)\left(\frac{f}{g}\right)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=−5x+3g(x) = -5x + 3\newlineChoices:\newline[A]All real numbers[\text{A]All real numbers}\newline[B]All real numbers except 35[\text{B]All real numbers except } \frac{3}{5}\newline[C]All real numbers except −35[\text{C]All real numbers except } -\frac{3}{5}\newline[D]All real numbers except 53[\text{D]All real numbers except } \frac{5}{3}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the inverse of the function.\newliney = −3x-3x \newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Find (f∘g)(0)(f \circ g)(0).\newlinef(x)=6xf(x) = 6x\newlineg(x)=x2+4xg(x) = x^2 + 4x\newline(f∘g)(0)=(f \circ g)(0) = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find (f∘g)(x)(f \circ g)(x).\newlinef(x)=x2+5f(x) = x^2 + 5\newlineg(x)=4xg(x) = 4x\newlineWrite your answer as a polynomial in simplest form.\newline(f∘g)(x)=(f \circ g)(x) = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Is f(x) f(x) the inverse function of g(x) g(x) ?\newlinef(x)=x f(x) = x \newlineg(x)=−4x g(x) = -4x \newlineChoices:\newline[yes] \text{[yes]} \newline[no] \text{[no]}
Get tutor helpright-arrow

Posted 1 month ago

Question
What is (f∗g)(x)(f * g)(x)? f(x)=3x2+9xf(x) = 3x^2 + 9x g(x)=3xg(x) = 3x Write your answer as a polynomial or a rational function in simplest form. ______
Get tutor helpright-arrow

Posted 2 months ago

View all (177)