Question

Given the function g(x)=4x+3 and g-¹ (15)=k, find the value of k

Answer 1

We know that g(x) = 4x + 3, and that the value of the inverse function of g(x), g^-1(x) has a value of k when its argument is 15.

We can solve it by first calculating the inverse function.

We can start by writing:

$\begin{gathered} g(x)=y\Rightarrow g^{-1}(y)=x \\ x=4y+3 \\ x-3=4y \\ \Rightarrow g^{-1}(x)=^{}y=\frac{x-3}{4} \end{gathered}$

Now, when the argument is x = 15, we get:

$\begin{gathered} g^{-1}(x)=\frac{x-3}{4} \\ g^{-1}(15)=\frac{15-3}{4}=\frac{12}{4}=3=k \\ \Rightarrow k=3 \end{gathered}$

Answer: k = 3