Question

I have a math test tomorrow and desperately need help with some questions. Could you answer this in the picture please

Answer 1

Step 1 : Given the function below

`h(x)=xg(x^2)+R^(-1)(x)`

Step 2: Write the function for h(3), this is done by substituting 3 for x in the function h(x) above

`\begin{gathered} h(x)=xg(x^2)+R^(-1)(x) \\ h(3)=3g(3^2)+R^(-1)(3)_{}_{} \\ h(3)=3* g(9)+R^(-1)(3)_{} \end{gathered}`

Step 3: Write the corresponding value for the function g(9) and an inverse function of R⁻¹ (3) on the table.

`\begin{gathered} g(9)\Rightarrow\text{ check the value of g(x) when x is 9} \\ g(9)=-5 \end{gathered}`
`\begin{gathered} R^(-1)(3)\Rightarrow\text{check the value of x when }R^(-1)\text{ is 3} \\ R^(-1)(3)=4^{} \end{gathered}`

Step 4: Substitute the g(9) and R⁻¹ (3) values in the h(3) equation and simplify

`\begin{gathered} h(3)=3* g(9)+R^(-1)(3) \\ h(3)=3*(-5)+4 \\ h(3)=-15+4 \\ h(3)=-11 \end{gathered}`

Hence, the value of h(3) is -11

The second option is the correct answer.