Reviewed by Maila Caliao
Which represents the inverse of the function f(x) = 4x? h(x) = x + 4, h(x) = x – 4, h(x) = 3/4 x, h(x) = 1/4 x
Answer: h(x) = 1/4 x represents the inverse of the function f(x) = 4x
Inverse functions undo the action of the original function. For a function like f(x) = 4x, its inverse h(x) must be a function that, when applied to f(x), returns the original input value x. Identifying the inverse involves reversing the operation carried out by the original function.
Methods
Math Tutor Explanation Using Algebraic Rearrangement
To find the inverse function, start with f(x) = 4x and solve for x in terms of y (where y = f(x)), then swap variables to write the inverse.
Step 1: Step 1: Set y = 4x
Step 2: Step 2: Solve for x: x = y / 4
Math Tutor Explanation Using Function Composition
Check which h(x) undoes f(x) when composed, returning x.
Step 1: Step 1: Substitute f(x) into each option for h(x)
Step 2: Step 2: h(f(x)) = h(4x). Try h(x) = 1/4 x: h(4x) = 1/4 * 4x = x
Step 1:
Step 2:
Math Tutor suggests: Practice with Inverse Functions and Related Algebra
Expand your understanding of inverse functions and related algebraic concepts with these exercises selected especially for you.
FAQ on Inverse Functions
What does it mean for two functions to be inverses?
Two functions are inverses if applying one after the other gets you back to your starting value: h(f(x)) = x and f(h(x)) = x.
How do you find the inverse of a linear function?
Solve the equation for x in terms of y, then swap x and y to write the inverse.
Why isn't h(x) = x + 4 the inverse of f(x) = 4x?
Because adding 4 does not undo multiplying by 4; only dividing by 4 or multiplying by 1/4 will reverse the operation.
Do all functions have inverses?
Only one-to-one functions have inverses that are also functions.
How can I check if my answer for an inverse is correct?
Compose the original function and your proposed inverse (in either order) and see if the result is x.
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