Function Composition and Inverses

Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))

• 19
• 23
• -10
• None of these.

Tags

CCSS.HSF-BF.A.1C

Tags

CCSS.HSF-BF.A.1C

When finding the inverse of a relation, 
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

• solve for y
• replace y with f^-1(x)
• solve for x
• find the greatest common factor

Tags

CCSS.HSF-BF.B.4A

What color matches the shape of the inverse of the following:

y = (x-3)² +1, x ≥ 3

• blue

• green

• orange

• red

• No inverse

Tags

CCSS.HSF-BF.B.4D

What color matches the shape of the inverse of the following:

y = (x-3)² +1, x ≤ 3

• blue

• green

• orange

• red

• No inverse

Tags

CCSS.HSF-BF.B.4D

• domain restriction x ≥ #

• domain restriction x ≤ #

• equation will be only the positive radical

• equation will be only the negative radical

Tags

CCSS.HSF-BF.B.4D

What must we consider for the inverse of the following

y = 3(x - 4)⁴ -7, x ≤ 4

• domain restriction x ≥ #

• domain restriction x ≤ #

• equation will be only the positive radical

• equation will be only the negative radical

• none

Tags

CCSS.HSF-BF.B.4D

Use a composition function to find the price of a $700 item after the discount, then the coupon.

(a)  

Answer explanation

To find the final price, apply the discount to the $700 item, then subtract the coupon. The correct answer format is $590, which matches the choice $590.

Tags

CCSS.HSF-BF.A.1C

• I only 

• I and II

• I and III

• I , II and III

Answer explanation

To find h(x) = f(g(x)), we need f(x) to be the outer function and g(x) the inner. I: f(x)=√x-7 and g(x)=x+5 works. III: f(x)=x-7 and g(x)=√(x+5) also works. II does not match the structure. Thus, I and III are correct.

Tags

CCSS.HSF-BF.A.1C

• {x ∣ x ≥ 1}

• {x ∣ x ≤ 1}

• {x ∣ x ≥ -3}

• {x ∣ x ≥ -1}