Fill in the blank(s) to correctly complete each sentence. If ƒ(x)...

Question

Fill in the blank(s) to correctly complete each sentence. If ƒ(x) = 4^x, then ƒ(2) = and ƒ(-2) = ________.

Accepted Answer

Hello, everyone. We've been asked to complete the sentence by filling in the blanks. We are told if F of X equals 12 raised to the X power, then F of three equals blank and F of negative three equals blank. Our answer choices are A F of three equals one over 1728 F of negative three equals 1728 B F of three equals 1728 F of negative three equals one over C F of three equals 36 F of negative three equals 1/36 D F of three equals 1/36 F of negative three equals 36. So let's take this step at a time starting with F of three. Recall that in function notation, when we have something like F of three, this means we want to put three in for X in the F of X function. So this would be 12 raised to the third power which is 12 cubed and 12 cubed is 728. So we know F F three is 1728. For F of negative three, we would have 12 raise the negative third power. Recall that a negative exponent moves our base to the other half of the fraction. So currently it's in the numerator. So I'm gonna move the 12 to the denominator, make our exponent positive and put a placeholder one in the numerator. So I now have 1/12 cubed. The one does not change and 12 cubed again is 1728. So what needs to be in the blanks? F of three equals 1728 F of negative three is one over 1728. And both of those are answer choice B have a nice day.

Struggling with College Algebra?

Fill in the blank(s) to correctly complete each sentence. If ƒ(x) = 4^x, then ƒ(2) = and ƒ(-2) = ________.

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