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If $f(x)=\sqrt{2 x-1},$ find $(a) f^{-1}(1)$,(b) $f^{-1}(3)$

(a) 1(b) 5

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

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Oregon State University

Baylor University

Lectures

01:54

If $f(x)=\sqrt{3 x+2},$ fi…

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If $f(x)=\frac{\sqrt{x}}{x…

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Find $f^{\prime}(x)$ if $f…

$$\text { If } f(x)=\frac{…

01:39

if f(x) = 2^(x-3). find f^…

so before we actually, um, try to figure out what these are One thing to always keep in mind. Anytime we're plugging something into these inverse functions, Sometimes values are not actually included in them. So something that is good to check is to find what is the range of your function over here to make sure that your inputs over here will be in the domain. Well, we know that the range of F is just going to be from zero to infinity because we know the square roots is 02 infinity them. We don't have any vertical changes. Um, which then would mean our domain of F inverse is also going to be 02 infinity. So that means both of these will be defined. Um, and the reason why I bring this up is because when we actually look for the inverse of this, there will be no restrictions on the domain with just how we have it written. So we just kinda have to keep this in mind because sometimes they might try to throw us for a loop because we could plug the number in, but it's not actually defined for that value. Yeah, But now let's go ahead and actually find within verses. And then we could just plug these in, though, So this would just be why? And then we change them out to be X is in between the square root of two Y minus one. So we square each side. Uh, that's minus. Then we're going to add one. So we have X squared plus one, and then we divide by two. So we have y and then this is f inverse of X. So we go ahead and plug one into here to be one square, so one plus 1/2, which would just be one. So that's that members of one and then down here at the inverse of three is going to be nine plus 1/2, which is going to be just five

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