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How do you find the inverse of #f(x)=2x+3#?

Answer 1

Lincoln Anderson

#g(x)=(x-3)/2# is the inverse of #f(x)=2x+3#

If #f(x) = 2x+3# then for any function #g(x)# #color(white)("XX")f(g(x)) = 2(g(x))+3#

If #g(x)# is the inverse of #f(x)# #color(white)("XX")f(g(x)) = x#

Therefore, if #g(x)# is the inverse of #f(x)# #color(white)("XX")2g(x)+3 =x#

#color(white)("XX")rarr 2g(x) = x-3#

#color(white)("XX")rarr g(x) = (x-3)/2#

Note that your instructor may have some special form they want you to use for the inverse of #f(x)#; for example #bar(f(x))# or #f^(-1)(x)#; if so replace #g(x)# with whatever form your instructor desires.

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Answer 2

Sophie Adams

To find the inverse of a function, (f(x)), we need to swap the roles of (x) and (y) and then solve for (y). The inverse function of (f(x)) is denoted as (f^{-1}(x)).

Given the function (f(x) = 2x + 3), let's first rewrite it in terms of (y):

[y = 2x + 3]

Now, we swap (x) and (y):

[x = 2y + 3]

Next, we solve this equation for (y):

[x - 3 = 2y] [y = \frac{x - 3}{2}]

So, the inverse function of (f(x) = 2x + 3) is:

[f^{-1}(x) = \frac{x - 3}{2}]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.