Question

If function $g:x\to 8-3x$, find the image of 5 and the pre image of 0.

Short answer

The image of 5 is $-7$ and the pre image of 0 is $\frac{8}{3}$ for the function.

Step-by-step solution

Step 1. Given Information.

Consider the given function is $g:x=8-3x$.

Step 2. Calculation.

Consider the given function $g:x=8-3x$. It can be also written as $g\left(x\right)=8-3x$.

To calculate the image of 5, substitute 5 for $x$ in the function.

$\begin{array}{c}g\left(5\right)=8-\left(3\times 5\right)\\ =8-15\\ =-7\end{array}$

To calculate the pre image, equate the function with the given value.

$\begin{array}{c}g\left(x\right)=0\\ 8-3x=0\\ x=\frac{8}{3}\end{array}$

Step 3. Conclusion.

Therefore, the image of 5 is $-7$ and the pre image of 0 is $\frac{8}{3}$ for the function.