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Find (a) the domain of f and (b) f -1 and its domain.

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Find (a) the domain of f and (b) f -1 and its domain.

asked Jan 27, 2015 in CALCULUS by anonymous

2 Answers

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(b)

Step 1:

The function is .

Consider image.

image

Interchange the variables image and image.

image

Above function is in the form image, where image.

The inverse function is image.

Step 2:

image

Solve for image.

Apply squaring on both sides.

image

Apply logarithm on each side.

image

The inverse function is image.

Step 3:

The inverse function is image.

The domain of a function is all values of x, those makes the function mathematically correct.

Since there should not be any negative numbers and zero in the logarithm function.

The expression image should be positive.

image

The domain of the inverse function is image.

Solution :

The inverse function is image.

The domain of the function is image.

answered Jan 27, 2015 by yamin_math Mentor
0 votes

(a)

Step 1:

The function is image.

The domain of a function is all values of x, those makes the function mathematically correct.

Since there shouldn't be any negative numbers in the square root.

The expression image should be zero or positive.

image

Apply logarithm on each side.

image

The domain of the function is image.

Solution :

The domain of the function is image.

answered Jan 28, 2015 by yamin_math Mentor

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