Question

I need help solving this problem The question started with H(x) = (x+7)^5

Answer 1

Answer

$g(x)=x+7$

Explanation

Given:

$\begin{gathered} The\text{ }composition\text{ }h\mleft(x\mright)=f\mleft(g\mleft(x\mright)\mright) \\ H(x)=(x+7)^5\text{ and }f(x)=x^5 \end{gathered}$

What to find:

Function g(x)

Step-by-step-solution:

To find g(x):

$\begin{gathered} If\text{ }f(x)=x^5,\text{ then} \\ f\lbrack g(x)\rbrack\Rightarrow x=g(x) \\ \text{Now }f\lbrack g(x)\rbrack=\lbrack g(x)\rbrack^5 \\ \therefore h(x)=f\lbrack g(x)\rbrack=\lbrack g(x)\rbrack^5=(x+7)^5 \\ \text{Hence, solve the equation by equating the base} \\ \lbrack g(x)\rbrack^5=(x+7)^5 \\ g(x)=x+7 \end{gathered}$