Question

If f(x) = -x + 8 and g(x) = x^4, what is (gºf)(2)?

Answer 1

`\bf \begin{cases} f(x)=&-x+8\\ g(x)=&x^4\\ (g\circ f)(x) =& g(~~f(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(2)=-(2)+8\implies f(2)=\boxed{6} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{(g\circ f)(2)}{g(~~f(2)~~)}\implies g\left( \boxed{6} \right) = (6)^4\implies \stackrel{(g\circ f)(2)}{g(6)} = 1296`

Answer 2

`\large\boxed{(g\circ f)(2)=1296}`

Explanation:

`(g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=\g\bigg(f(x)\bigg)=(-x+8)^4\\\\(g\circ f)(2)\to\text{put x = 2 to the equation}\ (g\circ f)(x):\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296`