How do you find the inverse of #f(x)= 5x + 10#?

Answer 1

To find the inverse of ( f(x) = 5x + 10 ), first, replace ( f(x) ) with ( y ). Then, switch the variables ( x ) and ( y ) to rewrite the equation as ( x = 5y + 10 ). Next, solve this equation for ( y ) in terms of ( x ).

( x = 5y + 10 )

( x - 10 = 5y )

( y = \frac{x - 10}{5} )

Therefore, the inverse function of ( f(x) = 5x + 10 ) is ( f^{-1}(x) = \frac{x - 10}{5} ).

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Answer 2

Savannah Anderson

The inverse of a function is the relation that is formed when the function is transformed over the line #y = x#

By substituting x for y and y for x in the equation, the inverse can be found algebraically; you will then need to isolate y.

#f(x) = 5x + 10#

#y = 5x + 10#

#x = 5y + 10#

#x - 10 = 5y#

#(x - 10)/5 = y#

So, #f^-1(x) = (x - 10)/5#

Practice tasks:

a) #f(x) = 3x + 4#

b) #g(x) = sqrt(4x - 1)#

c) #h(x) = 2/(2x - 3)#

Wishing you luck!

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.