# How do you find the inverse of #f(x)=2-3 log_4(x+1)#?

To find the inverse of ( f(x) = 2 - 3 \log_4(x+1) ):

- Replace ( f(x) ) with ( y ).
- Swap ( x ) and ( y ): ( x = 2 - 3 \log_4(y+1) ).
- Solve for ( y ).
- First, isolate the logarithmic term: ( 3 \log_4(y+1) = 2 - x ).
- Divide both sides by 3: ( \log_4(y+1) = \frac{2 - x}{3} ).
- Rewrite in exponential form: ( y+1 = 4^{\frac{2 - x}{3}} ).
- Subtract 1 from both sides: ( y = 4^{\frac{2 - x}{3}} - 1 ).

Therefore, the inverse of ( f(x) ) is ( f^{-1}(x) = 4^{\frac{2 - x}{3}} - 1 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Again, we get:

By signing up, you agree to our Terms of Service and Privacy Policy

Applying this here:

meaning

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- How do you find the asymptotes for #y = (7x-5)/(2-5x)#?
- How do you find vertical, horizontal and oblique asymptotes for #( x^2 + x - 5) /(4x - 8)#?
- How do you find the vertical, horizontal or slant asymptotes for #g(x)=(2x^2) / (x^2 - 5x - 6)#?
- How do you determine if #3sqrtx # is an even or odd function?
- How do you find vertical, horizontal and oblique asymptotes for #(3x^2+x-4) / (2x^2-5x)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7