Question

A function f is defined by

$f\left(x\right)=\frac{Ax+5}{6x-2}$

If$f\left(1\right)=4,$find A.

Short answer

The value of A is$11.$

Step-by-step solution

Step 1. Given Information

The given function is $f\left(x\right)=\frac{Ax+5}{6x-2}$

We have to find if$f\left(1\right)=4$then what is the value of A.

Step 2. Finding the value of A

Substitute the given values in the function

$$\begin{gathered} f\left(1\right)=\frac{A\left(1\right)+5}{6\left(1\right)-2} \\ 4=\frac{A+5}{6-2} \\ 4=\frac{A+5}{4} \\ 16=A+5 \\ 16-5=A \\ 11=A \end{gathered}$$