Question

MARKING AS BRAINLIEST!! Starr if given functions are inverse)!

Answer 1

Answer: f(x) and g(x) are inverses of each other

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Explanation:

Start with the f(x) function. Then plug in g(x) like so

$f(x) = 4x+3\\\\f(g(x)) = 4(g(x))+3\\\\f(g(x)) = 4\left(\frac{1}{4}x-\frac{3}{4}\right)+3\\\\f(g(x)) = 4\left(\frac{1}{4}x\right)+4\left(-\frac{3}{4}\right)+3\\\\f(g(x)) = x-3+3\\\\f(g(x)) = x$

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Now we'll start with the g(x) function and then plug in f(x)

$g(x) = \frac{1}{4}x-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(f(x))-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(4x+3)-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(4x)+\frac{1}{4}(3)-\frac{3}{4}\\\\g(f(x)) = x+\frac{3}{4}-\frac{3}{4}\\\\g(f(x)) = x$

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We've shown that the two equations are true

• f(g(x)) = x
• g(f(x)) = x

Therefore, f and g are inverses of each other.