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Function
m is defined by
m(x)=10 x. Function
n is defined by
n(x)=8x-3. Which of the following values of
x satisfies the functional equation
m(x)-n(x)=7 ?

Function $m$ is defined by $m(x)=10 x$ . Function $n$ is defined by $n(x)=8 x-3$ . Which of the following values of $x$ satisfies the functional equation $m(x)-n(x)=7$ ?

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Find the vertex of the transformed function

Full solution

Q. Function

m

is defined by

m(x)=10 x

. Function

n

is defined by

n(x)=8 x-3

. Which of the following values of

x

satisfies the functional equation

m(x)-n(x)=7

?

Define functions and equation: Define the functions $m(x)$ and $n(x)$ and set up the equation according to the problem statement. $m(x) = 10x$ $n(x) = 8x - 3$ Set up the equation: $m(x) - n(x) = 7$ $10x - (8x - 3) = 7$
Simplify equation: Simplify the equation by distributing and combining like terms. $\newline$ $10x - 8x + 3 = 7$ $\newline$ $2x + 3 = 7$
Solve for x: Solve for x by isolating the variable. $\newline$ $2x + 3 = 7$ $\newline$ $2x = 7 - 3$ $\newline$ $2x = 4$ $\newline$ $x = \frac{4}{2}$ $\newline$ $x = 2$

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