Question

Two functions represent the composite function h(x) = (x - 1)3 + 10 so that h(x) = (g p(x). Given f(x) = x + a andg(x) = x3 + b, what values of a and b would make the composition true?a=b =

Answer 1

Given:-

`h\mleft(x\mright)=(x-1)^3+10,f(x)=x+a,g(x)=x^3+b`

To find the value of a and b when the composition is true.

So now we simplfiy,

`\begin{gathered} (gof)(x)=g(f(x)) \\ =(x+a)^3+b \end{gathered}`

So now we equate. we get,

`(x-1)^3+10=(x+a)^3+b_{}`

So the required value is,

`a=-1,b=10`