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What is the inverse of the function #f(x) = 7log_4(x+3) - 2#? It is #7log_4 (x+3) - 2#, if that clears any confusion.

Answer 1

Kennedy Adams

#g(x) = 4^{(x+2)/7}-3#

Calling #f(x) = 7log_4(x+3) - 2# we have

#f(x) = log_4((x+3)^7/4^2) = y#

Now we will proceed to obtain #x = g(y)#

#4^y = (x+3)^7/4^2# or
#4^{y+2} = (x+3)^7#
#4^{(y+2)/7}=x+3# and finally
#x = 4^{(y+2)/7}-3 = g(y) = (g@f)(x)#

So #g(x) = 4^{(x+2)/7}-3# is the inverse of #f(x)#

Attached a plot with #f(x)# in red and #g(x)# in blue.

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Answer 2

Abigail Allen

Swap x and y, then solve for y to find the inverse: (f^{-1}(x) = 4^{(10(x+2))/7}).

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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.

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.

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.

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.

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