Home > Precalculus > Modeling with Functions

If f(x) = 7-2x and g(x) = x+3 . A. What is g^-1 (x) ? B. What is f(g^-1(5)) ?

Answer 1

Liam Brennan

#g^-1(x)=x-3#
#f(g^-1(5))=3#

#Def. g^-1(g(x))=x#

#g^-1(x+3)=x#

#x+3=t => x=t-3#

#g^-1(t)=t-3#

#g^-1(x)=x-3#

#g^-1(5)=5-3=2#

#f(g^-1(5))=f(2)=7-2*2=3#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Elias Ackerman

A. The inverse function ( g^{-1}(x) ) of ( g(x) = x + 3 ) can be found by interchanging ( x ) and ( y ) in the equation ( y = x + 3 ) and then solving for ( y ). ( y = x + 3 ) Interchanging ( x ) and ( y ): ( x = y + 3 ) Solving for ( y ): ( y = x - 3 ) Therefore, ( g^{-1}(x) = x - 3 ).

B. To find ( f(g^{-1}(5)) ), we substitute ( g^{-1}(5) ) into ( f(x) = 7 - 2x ). ( f(g^{-1}(5)) = 7 - 2 \times (g^{-1}(5)) ) Since ( g^{-1}(5) = 5 - 3 = 2 ), ( f(g^{-1}(5)) = 7 - 2 \times 2 = 7 - 4 = 3 ). Therefore, ( f(g^{-1}(5)) = 3 ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.