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=(x-3)/(4) \end{gathered}`

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

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

Answer: k = 3