If f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?

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abidemiokin abidemiokin · Answer 1 · 2021-08-19T15:27:48+02:00

The equivalent to (g-f)(3) if f(x)=4-x^2 and g(x)=6x is 23

Composite functions are functions that are written inside another function. We can also refer to them as a function of a function.

Given the expressions

[tex]f(x)=4-x^2 \\g(x)=6x[/tex]

What we are to find is (g-f)(3). But first, we need to get (g-f)(x)

(g-f)(x) = g(x) - f(x)

(g-f)(x) = 6x - (4-x²)

Expand then bracket:

(g-f)(x) = 6x - 4 + x²

Next is to get (g-f)(3) by substituting x = 3 into the resulting function

(g-f)(3) = 6(3) - 4 + (3)²

(g-f)(3) = 18 - 4 + 9

(g-f)(3) = 14 + 9

(g-f)(3) = 23

Hence the equivalent to (g-f)(3) if f(x)=4-x^2 and g(x)=6x is 23.

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joaobezerra joaobezerra · Answer 2 · 2021-09-17T16:34:34+02:00

Subtracting the functions, it is found that the equivalent expression to (g-f)(3) is given by:

[tex]6(3) - 4 + 3^2[/tex], which is the third option.

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The functions are:

[tex]g(x) = 6x[/tex]

[tex]f(x) = 4 - x^2[/tex]

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The subtraction function is:

[tex](g - f)(x) = g(x) - f(x) = 6x - (4 - x^2) = 6x - 4 + x^2[/tex]

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The equivalent expression at x = 3 is given by:

[tex](g - f)(3) = 6(3) - 4 + 3^2[/tex], which is the third option.

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