Question

Evaluate the piecewise function at the given values of the independent variableFind A B C

Answer 1

Based on the piecewise function, we have two conditions: if x is equal to 5 and not equal to 5.

Since the given value of x in the question is 3, let's use the first condition that states x is not equal to 5.

`h(x)=(x^2-25)/(x-5)`

Let's plug in x = 3 in the function above.

`h(3)=(3^2-25)/(3-5)`

Then, simplify.

`\begin{gathered} h(3)=(9-25)/(-2) \\ h(3)=(-16)/(-2) \\ h(3)=8 \end{gathered}`

Therefore, h(3) = 8.

Similary, for B, since the given value of x is 0, which is not equal to 5 still, let's use the first condition and plug in x = 0.

`\begin{gathered} h(x)=(x^2-25)/(x-5) \\ h(0)=(0^2-25)/(0-5) \\ h(0)=(-25)/(-5) \\ h(0)=5 \end{gathered}`

Hence, h(0) = 5.

Lastly, for C, the given value of x is 5. With that, we shall use the second condition.

`\begin{gathered} h(x)=4 \\ h(5)=4 \end{gathered}`

Therefore, h(5) = 4.