What is the inverse of the function f(x) = 2x + 1?
2 answers:
Answer:
(a) h(x) = 1/2x -1/2
Step-by-step explanation:
The inverse of the function y = f(x) is found by solving x = f(y).
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<h3>setup</h3>
x = f(y)
x = 2y +1 . . . . . . use the definition of f(x)
<h3>solution</h3>
x -1 = 2y . . . . . subtract 1
(x -1)/2 = y . . . . divide by 2
y = 1/2x -1/2 . . . . eliminate parentheses
h(x) = 1/2x -1/2 . . . write in functional form
The inverse of f(x) = 2x+1 is ...
h(x) = 1/2x -1/2
Step-by-step explanation:
for the inverse function we simply try to turn y and x around, and find the equation that calculates x out of y instead of y out of x.
remember,
f(x) = y
so, we have
y = 2x + 1
y - 1 = 2x
x = y/2 - 1/2
now we just rename x to y and y to x to make this a "normal" function :
y = h(x) = x/2 - 1/2
so, the first answer option is correct.
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