Step 1 : Given the function below
[tex]h(x)=xg(x^2)+R^{-1}(x)[/tex]
Step 2: Write the function for h(3), this is done by substituting 3 for x in the function h(x) above
[tex]\begin{gathered} h(x)=xg(x^2)+R^{-1}(x) \\ h(3)=3g(3^2)+R^{-1}(3)_{}_{} \\ h(3)=3\times g(9)+R^{-1}(3)_{} \end{gathered}[/tex]
Step 3: Write the corresponding value for the function g(9) and an inverse function of R⁻¹ (3) on the table.
[tex]\begin{gathered} g(9)\Rightarrow\text{ check the value of g(x) when x is 9} \\ g(9)=-5 \end{gathered}[/tex][tex]\begin{gathered} R^{-1}(3)\Rightarrow\text{check the value of x when }R^{-1}\text{ is 3} \\ R^{-1}(3)=4^{} \end{gathered}[/tex]
Step 4: Substitute the g(9) and R⁻¹ (3) values in the h(3) equation and simplify
[tex]\begin{gathered} h(3)=3\times g(9)+R^{-1}(3) \\ h(3)=3\times(-5)+4 \\ h(3)=-15+4 \\ h(3)=-11 \end{gathered}[/tex]
Hence, the value of h(3) is -11
The second option is the correct answer.
