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01.07.2022 - 03:16

Evaluate the function f(x)=x^2+6x-9 at the given values of the independent variable and simplify. a. f(-6) b. f(x+9) c. f(-x)

Question:

Evaluate the function {eq}f(x)=x^2+6x-9 {/eq} at the given values of the independent variable and simplify.

a. {eq}f(-6) {/eq}

b. {eq}f(x+9) {/eq}

c. {eq}f(-x) {/eq}

Answers (1)

Lora April 5, 2023 в 09:20

a. To evaluate {eq}f(x)=x^2+6x-9 {/eq} at {eq}x=-6 {/eq}, we substitute -6 for x: {eq}f(-6) = (-6)^2 + 6(-6) - 9 = 36 - 36 - 9 = -9 {/eq} b. To evaluate {eq}f(x)=x^2+6x-9 {/eq} at {eq}x + 9 {/eq}, we substitute {eq}x+9 {/eq} for x: {eq}f(x+9) = (x+9)^2 + 6(x+9) - 9 {/eq} Expanding the square and simplifying, we get: {eq}f(x+9) = x^2 + 24x + 72 {/eq} c. To evaluate {eq}f(x)=x^2+6x-9 {/eq} at {eq}-x {/eq}, we substitute -x for x: {eq}f(-x) = (-x)^2 + 6(-x) - 9 = x^2 - 6x - 9 {/eq}

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