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Determine whether or not the function determined by the given equation is one-to-one.$$G(x)=-3 x+7$$

Yes

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

University of Michigan - Ann Arbor

Idaho State University

Lectures

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00:52

to see if this is a 1 to 1 function. What we can do is first start by plugging into just to arbitrary numbers A and B and then seeing if we could come to the conclusion that A and B have to be the same number. And if that holds, then we know it is 1 to 1. So let's go ahead and start. Um, so we're going to start with G of A is equal to G of B so g of a what we just replace the extra face would be negative. Three A plus seven isn't too the negative three B plus seven for J B. And now we just want to try to solve for A and B earliest, get them in terms of each other. So we have find a seven on each side. So those canceled and we're gonna be left with negative three A is equal to negative three B. Then we can go ahead and divide each side by negative three. The negative threes Council. Then we just have a is equal to be so since a is equal to be, this is want one. So yes, g a fax one toe one, and then you could put your little fruit box and smiley face because you're glad you're done with it.

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