Answer:
[tex]h(-3)=\boxed{\dfrac{5}{4}}[/tex]
[tex]h(2)=\boxed{3}[/tex]
[tex]h(5)=\boxed{-\dfrac{19}{4}}[/tex]
Step-by-step explanation:
Given piecewise function:
[tex]h(x) \begin{cases} -\dfrac{3}{4}x-1\; &\text{if}\;x\neq 2\\\\3 \; &\text{if}\;x=2 \end{cases}[/tex]
To find h(-3), substitute x = -3 into the function:
[tex]\begin{aligned}\implies h(-3)&=-\dfrac{3}{4}(-3)-1\\\\&=\dfrac{9}{4}-1\\\\&=\dfrac{9}{4}-\dfrac{4}{4}\\\\&=\dfrac{5}{4}\end{aligned}[/tex]
To find h(2), substitute x = 2 into the function:
[tex]\implies h(2)=3[/tex]
To find h(5), substitute x = 5 into the function:
[tex]\begin{aligned}\implies h(5)&=-\dfrac{3}{4}(5)-1\\\\&=-\dfrac{15}{4}-1\\\\&=-\dfrac{15}{4}-\dfrac{4}{4}\\\\&=-\dfrac{19}{4}\end{aligned}[/tex]
