SOLUTION: Fill in Table A for the exponential function y=3^x Use the "inverse property" to fill in Table B.
Table A- (x)[-1,0,1,2] (y=3^x)[MUST FILL IN]
Table B-(x)[MUST FILL IN] (i
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Question 1140124: Fill in Table A for the exponential function y=3^x Use the "inverse property" to fill in Table B.
Table A- (x)[-1,0,1,2] (y=3^x)[MUST FILL IN]
Table B-(x)[MUST FILL IN] (inverse)[MUST FILL IN]
b. Plot the points from TABLE B t sketch a graph of the inverse
c. Use your graph from (b) to give the natural domain and range of the inverse
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Table A-
|
|...
|........
|.......
|........
Table B-
first find the inverse:
........swap and
..........solve for , take a log of both sides
|
|.............->no real solution
|.............->-∞
|.............
|.............
b. Plot the points from TABLE B t sketch a graph of the inverse
c. Use your graph from (b) to give the natural domain and range of the inverse
domain :{ element : } (all positive real numbers)
and
range: (all real numbers)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
y = 3^x
:
domain of this function is all real numbers, the function does not cross the x-axis, therefore there are no roots (x-intercepts)
:
here is a graph of the equation y = 3^x
:
:
the real solution for the inverse, interchange x and y and solve for y
:
x = 3^y
:
take the natural logarithm of both sides of =
:
ln(x) = y * ln(3)
:
y = ln(x)/ln(3)
:
f^(-1) (x) = ln(x)/ln(3) for x > 0
:
here is a graph of the inverse
:
:
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