Question

Evaluate the function f(x)=6x+2 at the given values of the independent variable and simplify.

a. f(8) b. f(x+6) c. f(−x)
. f(8)= (Simplify your​ answer.)

Answer 1

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`\longmapsto \: f(x) = 6x + 2`

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A.
`f(8) = 6(8) + 2 = 48 + 2 = \boxed{ 50}✓`

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B.
`f(x + 6) = 6(x + 6) + 2 \\ = 6x + 36 + 2 \\ = \boxed{ 6x + 38}✓`

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C.
`f( - x) = 6( - x) + 2 = \boxed{ - 6x + 2}✓`

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Answer 2

`f(x) = 6x+2`

A.

To evaluate f(8), we substitute x with 8 in our expression.

`f(8) = 6*8 + 2\\f(8) = 48 +2\\f(8) = 50`

Answer: f(8) = 50

B.

To evaluate f(x+6), we do the same but substitute x with x+6 instead.

`f(x+6) = 6(x+6) + 2`

Expand the parenthesis by multiplying 6 with x and 6.

`f(x+6) = 6x + 6*6 + 2\\f(x+6) = 6x+36+2\\f(x+6) = 6x+38`

Answer: f(x+6) = 6x + 38

C.

Again, we're doing the same thing, just substituting x with -x.

`f(-x) = 6 * (-x) + 2\\ f(-x)=-6x+2`

Answer: f(-x) = -6x+2