Question

if (f(x)=x + 8) and (g(x)=x - 8), (a) (f(g(x))=) (b) (g(f(x))=) (c) thus (g(x)) is called an function of (f(x)) question help: video

Explanation:

Step1: Find $f(g(x))$

Substitute $g(x)$ into $f(x)$. Given $f(x)=x + 8$ and $g(x)=x - 8$, then $f(g(x))=(x - 8)+8$.

Step2: Simplify $f(g(x))$

$(x - 8)+8=x-8 + 8=x$.

Step3: Find $g(f(x))$

Substitute $f(x)$ into $g(x)$. Given $g(x)=x - 8$ and $f(x)=x + 8$, then $g(f(x))=(x + 8)-8$.

Step4: Simplify $g(f(x))$

$(x + 8)-8=x+8 - 8=x$.

Step5: Determine the relationship

Since $f(g(x))=x$ and $g(f(x))=x$, $g(x)$ is the inverse function of $f(x)$.

Answer:

(a) $x$
(b) $x$
(c) inverse