Function Operations

Use functions f(x) and g(x) to answer the questions f(x)=(x-5)2;g(x)=4x

What is (5g+f)(-2)? (5g+f)(x)=x2+10x+25 (5g+f)(-2)=(-2)2+10(-2)+25 =4+10(-2)+25 =4-20+25 =9

Use functions f(x) and g(x) to answer the questions f(x)=(x-5)2;g(x)=4x

What is (5g+f)(x)? (5g+f)(x)=5g(x)+f(x) =5(4x)+(x-5)2 =20x+x2-10x+25 =x2+10x+25

Use functions f(x) and g(x) to answer the questions f(x)=(x-5)2;g(x)=4x

What is (g-f)(1)? (g-f)(x)=-x2+14x-25 (g-f)(1)=-1 squared+14(1)-25 =-1+14(1)-25 =-1+14-25 =-12

Use functions f(x) and g(x) to answer the questions f(x)=(x-5)2;g(x)=4x

What is (g-f)(x)? (g-f)(x)=g(x)-f(x) =4x-(x-5)2 =4x-(x2-10x+25) =4x-x2+10x-25 =-x2+14x-25

Pages 119-120 through example 3

complete problems 1-4 and 9-12 on pages 122-123

What is equal to (f+g)(4)?

f(x)=(x-2)2;g(x)=x+3 11

Which answer is equal to (f-g)(-5)?

f(x)=2+x;g(x)=x2+5 -33

What is the domain of (f/g)(x)?

f(x)=5-x square root;g(x) x+5 square root {x|-5<x<5}

Which expression is equal to (fg)(x)?

f(x)=x+6;g(x)=x2-2 x3+6x2-2x-12

Which expression is equal to (f+g)(x)?

f(x)=x2+10;g(x)=x-3 x2+x+7

Youtube video

https://youtu.be/mMw_AUzCv5o

You can add, subtract, multiply, and divide functions much the same way you do with numbers. When dividing, remember to omit any values of x that make the denominator zero. To evaluate combinations of functions, you can first perform the operation on the functions. Then you can evaluate the new function for the given value.

(f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (f*g)(x)=f(x)*g(x) (f/g)(x)=f(x)/g(x)

Determine the domain of (f/g) (x) when f(x)= x+2 square root and g(x)=x2-9 square root

Domain of f:{x|x≥−2} Domain of g:{x|x≤−3 or x≥3} Intersection of Domains: {x|x≥3} Exclude 3 because it makes the denominator equal to 0. The domain of (f/g) (x) is {x|x>3}