Manisha M.

USC Tutor for Math and Business

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Pre-Calculus

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Question:

If f(x)=5x-8, find a formula for f^{-1}(y).

Manisha M.

Answer:

Let y=5x-8. Then y+8=5x, so x=1/5(y+8) and therefore f^{-1}(y)=1/5(y+8).

Calculus

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Question:

Differentiate: y=sin(5x)

Manisha M.

Answer:

The outer layer is ``the sine function'' and the inner layer is (5x) . Differentiate ``the sine function'' first, leaving (5x) unchanged. Then differentiate (5x). D(sin(5x))= cos(5x) D(5x) = cos(5x) 5 = 5cos(5x)

Algebra

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Question:

Find the slope of the line: 5x - 5y = 7

Manisha M.

Answer:

Given the line 5x - 5y = 7 Rewrite the equation in slope intercept form y = mx + b and identify the value of m the slope. -5y = -5x + 7 y = x - 7/5 The slope is given by the coefficient of x which is 1.

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