Question

If h(x) = fle" class="latex-formula"> ° $g) (x)$ and $h(x) = \sqrt[3]{x+3}$, find $g(x)$ if $f(x) = \sqrt[3]{x +2}$ ·

Answer 1

Answer:

g(x) = x+1

Step-by-step explanation:

f(x) = $\sqrt[3]{x+2}$

h(x) =$\sqrt[3]{x+3}$

h(x)= (fog)(x)= f(g(x))= $\sqrt[3]{g(x)+2}$

so   $\sqrt[3]{x+3}$ =$\sqrt[3]{g(x)+2}$

    cubing both sides ,we get

      x+3 = g(x)  +2

      solving for g(x) ,we get

g(x) = x+1