Question

I need help to do these composition of functions. I have a photo if needed.h(a)=4a+1g(a)=2a-5Find (h×g)(-9)

Answer 1

The composition of two functions is defined as follows:

`(h\circ g)(x)=h(g(x))`

Use the given rules of correspondence of h and g to find the composition of those two functions. Then, evaluate the composition at -9:

`\begin{gathered} h(a)=4a+1 \\ \Rightarrow h(g(a))=4\cdot g(a)+1 \end{gathered}`
`\begin{gathered} g(a)=2a-5 \\ \Rightarrow4\cdot g(a)+1=4\cdot(2a-5)+1 \\ =8a-20+1 \\ =8a-19 \end{gathered}`

Then:

`\begin{gathered} (h\circ g)(a)=h(g(a)) \\ =4\cdot g(a)+1 \\ =8a-19 \\ \\ \therefore(h\circ g)(a)=8a-19 \end{gathered}`

Evaluate the composition of h and g at a=-9:

`\begin{gathered} (h\circ g)(-9)=8(-9)-19 \\ =-72-19 \\ =-91 \end{gathered}`

Therefore:

`(h\circ g)(-9)=-91`