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A day full of math games & activities. Find one near you.
Given the function f(x) = 5(x+4) - 6, solve for the inverse function when x = 19?
72, 1, 84, 68
Solution:
Given: Function f(x) = 5(x + 4) - 6
An inverse function reverses the operation done by a particular function.
In other words, the inverse function undoes the action of the other function.
First replace f(x) with y.
y = 5(x + 4) - 6
Using the multiplicative distributive property,
y = 5x + 20 - 6
y = 5x + 14
Replace x with y and y with x.
x = 5y + 14
Solving for y, we get,
5y = x - 14
y = (x - 14)/5
Finally replace y with f -1(x).
f -1(x) = (x - 14)/5
Given x = 19,
y = (19 - 14)/5
y = 5/5
y = 1
Verification:
(f ∘ f -1)(x)= x
(f ∘ f -1)(x)= f [ f -1(x)]
= f [(x - 14)/5]
= f [x/5 - 14/5]
= 5[x/5 - 14/5] +14
= x - 14 + 14
= x
Therefore, the inverse function when x = 19 is 1.
Given the function f(x) = 5(x + 4) - 6, solve for the inverse function when x = 19?
Summary:
If the function f(x) = 5(x + 4) - 6, then the inverse function when x = 19 is 1.
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