Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = (x + 4) / 6, g(x) = 6x - 4

Solution:

Inverse means the opposite effect of an action or a step. In mathematics, we have operations such as addition(+), subtraction(−), multiplication(×), division(÷), squaring, square root, and logarithms.

When we use two operations together, it is possible to have an inverse impact on the result due to the operations used.

The process in which the effect of one operation is inversed by another operation is termed as inverse operations.

Given, f(x) = (x + 4) / 6

g(x) = 6x - 4

To find f(g(x))

f(g(x)) = f(6x - 4)

= [(6x - 4) + 4] / 6

= 6x / 6

= x

f(g(x)) = x

To find g(f(x))

g(f(x)) = g((x + 4) / 6)

= 6((x + 4) / 6) - 4

= x + 4 - 4

= x

g(f(x)) = x

Therefore, f(g(x)) = g(f(x)) = x

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Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = (x + 4) / 6, g(x) = 6x - 4

Summary:

If f(x) = (x + 4) / 6 and g(x) = 6x - 4, f and g are inverses as f(g(x)) = g(f(x)) = x.