Question

Suppose that the function h is defined, For all real numbers, as follows

Please help

Answer 1

`h(-3)=\boxed{(5)/(4)}`

`h(2)=\boxed{3}`

`h(5)=\boxed{-(19)/(4)}`

Explanation:

Given piecewise function:

`h(x) \begin{cases} -(3)/(4)x-1\; &\text{if}\;x\\eq 2\\\\3 \; &\text{if}\;x=2 \end{cases}`

To find h(-3), substitute x = -3 into the function:

`\begin{aligned}\implies h(-3)&=-(3)/(4)(-3)-1\\\\&=(9)/(4)-1\\\\&=(9)/(4)-(4)/(4)\\\\&=(5)/(4)\end{aligned}`

To find h(2), substitute x = 2 into the function:

`\implies h(2)=3`

To find h(5), substitute x = 5 into the function:

`\begin{aligned}\implies h(5)&=-(3)/(4)(5)-1\\\\&=-(15)/(4)-1\\\\&=-(15)/(4)-(4)/(4)\\\\&=-(19)/(4)\end{aligned}`

Answer 2

• 5/4; 3; - 19/4

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Find the following:

• h(-3) = (- 3/4) * (- 3) - 1 = 9/4 - 1 = 5/4, since x ≠ 2
• h(2) = 3, since x = 2
• h(5) = (- 3/4) * 5 - 1 = - 15/4 - 1 = - 19/4, since x ≠ 2