Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

(b) 
f(x)=x+2

{:[g(x)=x+2],[f(g(x))=◻],[g(f(x))=◻]:}

f and 
g are inverses of each other

f and 
g are not inverses of each other

(b) f(x)=x+2 f(x)=x+2 \newlineg(x)=x+2f(g(x))=g(f(x))= \begin{array}{l} g(x)=x+2 \\ f(g(x))=\square \\ g(f(x))=\square \end{array} \newlinef f and g g are inverses of each other\newlinef f and g g are not inverses of each other

Full solution

Q. (b) f(x)=x+2 f(x)=x+2 \newlineg(x)=x+2f(g(x))=g(f(x))= \begin{array}{l} g(x)=x+2 \\ f(g(x))=\square \\ g(f(x))=\square \end{array} \newlinef f and g g are inverses of each other\newlinef f and g g are not inverses of each other
  1. Calculate f(g(x))f(g(x)): Step 11: Calculate f(g(x))f(g(x)).\newlineSubstitute g(x)g(x) into f(x)f(x).\newlinef(g(x))=f(x+2)=(x+2)+2=x+4f(g(x)) = f(x + 2) = (x + 2) + 2 = x + 4.
  2. Calculate g(f(x))g(f(x)): Step 22: Calculate g(f(x))g(f(x)).\newlineSubstitute f(x)f(x) into g(x)g(x).\newlineg(f(x))=g(x+2)=(x+2)+2=x+4g(f(x)) = g(x + 2) = (x + 2) + 2 = x + 4.
  3. Check results: Step 33: Check if f(g(x))f(g(x)) and g(f(x))g(f(x)) equal xx.\newlinef(g(x))=x+4f(g(x)) = x + 4 and g(f(x))=x+4g(f(x)) = x + 4.\newlineBoth are not equal to xx; they are x+4x + 4.

More problems from Even and odd functions