Question

Will someone please check my answers? I don't think i have them right. The lab is attached

Answer 1

@ranga

Answer 2

\(f(x) = a^x\) has domain \([-\infty, \infty)\). But the range is \((0, \infty)\).

Answer 3

Did I mess up drawing the inverse also?

Answer 4

Yes, the function is one to one because it passes the horizontal line test where a horizontal line drawn anywhere intersects the curve at no more than one point. So an inverse exists.

Answer 5

For the domain on f(x)=a^x I don't write it with open parenthesis?

Answer 6

that should be ( ). typo.

Answer 7

No worries! The graph inverse is right or no?

Answer 8

Looks right to me. Just imagine (or draw) a 45 degree line (that is, y = x) and the inverse will be a reflection of f(x) on that line.

Answer 9

Sorry for all the questions!#3 is okay?

Answer 10

For 1) D: (-infinity, infinity) R: (0, infinity)
For 3) D: (0,infinity) R: (-infinity, infinity)

The domain and the range switch places between f(x) and its inverse.

Answer 11

Last question when writing the domain of 0 do I use [0, infinity) or (0, Infinity)?

Answer 12

f(x) asymptotically approaches zero but never quite touches zero.
So it should be (0.

Answer 13

Got it! Thanks for your help!!

Answer 14

You are welcome.

Answer 15

Hi! I missed the question on the very bottom of the page on how to find a formula for the graph? If you come online can you please explain how I find that? I can't figure it out. Thanks again fir your help!

Answer 16

They are asking for the inverse function.

Original function is \(\Large y = a^x\)
To find its inverse, interchange x and y and solve for y.
Interchange x and y: \(\Large x = a^y\)
Solve for y: Take logarithm on both sides to the base 'a':
\(\Large \log_a(x) = \log_a(a^y) = y\log_a(a) = y \)

Inverse function is \(\Large y = \log_a(x) \)

Answer 17

Thank you so much!