Question

Find the domain, x and y intercepts and inverse for f(x) = 4log9x+2)-3

Answer 1

is it \[\log_{9} x \]or \[\log (9x)\]

Answer 2

Also, why is there an extra parenthesis?

Answer 3

sorry, the 9 was supposed to be a parenthesis. So the question is Find the domain, x and y intercepts and inverse for f(x) = 4log(x+2)-3

Answer 4

the log is it log base 10 or log base e

Answer 5

log base 10 I would guess since usually they use ln if it brings up e

Answer 6

\[f(x) = 4 \log_{10} (x + 2) - 3\]The domain would be x > -2 because logarithm cannot take a negative value.

Answer 7

For x-intercept, let f(x) = 0 and solve for x. For y-intercept, let x = 0 and solve for f(0).

Answer 8

For inverse
Let \[y = f ^{-1}(x)\]\[f(y) = ff^{-1}(x)\]\[4\log_{10}(y + 2) - 3 = x \]\[4\log_{10}(y + 2) = x + 3 \]\[\log_{10}(y + 2) = \frac{ x + 3 }{ 4 } \]\[y + 2 = 10^{\frac{ x + 3 }{ 4 }}\]\[y = 10^{\frac{ x + 3 }{ 4 }} - 2\]\[f ^{-1}(x) = 10^{\frac{ x + 3 }{ 4 }} - 2\]

Answer 9

By the way, the domain of f inverse is the range of f.

Answer 10

which is \[x \in (-\infty , \infty)\]

Answer 11

Would the x-intercept be -3?

Answer 12

*y-intercept

Answer 13

No

Answer 14

great -_-