Answer: D) h(x) = (1/4)x
This is the same as h(x) = x/4
In decimal form, it would be h(x) = 0.25x
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Explanation:
Inverses undo the original function. The original function tells us to take any input (x) and multiply by 4 to get the output y = f(x) = 4x
To get the inverse, we reverse the operation applied here. The opposite of multiplication is division. So we'll divide by 4 instead of multiply by 4. This is why the answer is x/4 or (1/4)x
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Another approach is to do the following: Replace f(x) with y. Swap x and y. Solve for y
f(x) = 4x
y = 4x
x = 4y
4y = x
y = x/4
h(x) = x/4
We end up with the same result as before.
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Extra info:
For any real number x, the following two equations are true
h( f(x) ) = x
f( h(x) ) = x
