What should the domain of g(x) (the red graph) be limited to if f(x) and g(x) are inverses? f(x) = −3+√√x + 7 Domain of g(x) should be limited to:

Let f(x)=2x+8, g(x)=x^2+2x-8, and 3x-6 Preform the indicated operation. (Simplify as far as possible.) (f+g)(x)=

If f(x) = x^2 + 7 and g(x) = Square root of x + 8,a. find and simplify (fog)(x) and write its domain in interval notation.b. find and simplify (gof)(x) and write its domain in interval notation.

CHECK Your Unde 1. Simplify. a) (3x² - 7x + 5) + (x²-x + 3) b) (x² - 6x + 1)-(-x² - 6x + 5) c) (2x² - 4x + 3) - (x²-3x + 2) + (x² - 1) 2. Show that f(x) and g(x) are equivalent by simplifying each. 3. Show that f(x) and g(x) are not equivalent by evaluating each function. suitable value of x. PRACTISING 4. Simplify. b) a) (2a + 4c + 8) + (7a-9c-3) (3x + 4y - 5z) + (2x² + 6z) (6x + 2y + 9) + (-3x - 5y - 8) (2x² - 7x + 6) + (x² - 2x - 9) c) f) d) f(x) = (2x-1)-(3-4x) + (x + 2) g(x) = (x + 6) + (6x9) (-2x - 1) e) f) (x² + y² + 8) + 5. Simplify. a) (m-n+2p) - (3n+p-7) b) (-6m 2q + 8) (4a²-9) - (a³ + 2a-9) 6. Simplify. a) b) (-4x² - 2xy) + (6x²-3xy + 2y²) (4x² - 2y² - 9) f(x) = 2(x 3) + 3(x − 3) g(x) = 5(2x - 6) c) d) (2m² - 6mn + 8n²) + (4m² + mn + (3x² + 2y² + 7) - (4x² - 2y² - 8) f) 5x² - (2x² +30) + (-20) e) -x+ 2 (2x-y)-(-3x + 4y) + (6x-2y) (3x²2x) + (x² - 7x) - (7x + 3) c) (2x² + xy - y²) - (x² + 4xy + y²) + (3x² - 5xy) (xy - xz + 4yz) + (2x - 3yz) - (4y - xz) d) 1 e) 3 (2m + 2q + 7)…

show that the difference quotient of f(x)=square root of x can be written as 1/the square root of x+h + the square root of x.

Need only handwritten solution only (not typed one).

A quadratic function is defined by f(x) =x^2+(k+2)x-12 where k is a constant. It is given that the equation f(x) = 0 has two distinct real roots. Find the set of values that k can take.

If h(x) = 2. 2x and g(x) = x², find h(g(x)). Do not simplify. O h(g(x)) = 2æx? Oh(g(x)) = h(2æ²) h(2a²) Oh(g(a)) = 2x(a) O h(g(x)) = 2² Oh(g(x)) = (2x)? Question Help: DVideo Calculator Submit Question

1a. f(x)=−x^2 ; g(x)=x−3Find the expressions for f∘g and g∘f and give their domains.(f∘g)(x)=Domain (in interval notation):   (g∘f)(x)=Domain (in interval notation): 1b. f(x)=√x−2 ; g(x)=3x+1Find the expressions for f∘g and g∘f and give their domains.(f∘g)(x)=Domain (in interval notation):    (g∘f)(x)=Domain (in interval notation): 1c. f(x)=|x| ; g(x)=x/x−5Find the expressions for f∘g and g∘f and give their domains.(f∘g)(x)=  Domain (in interval notation):    (g∘f)(x)=  Domain (in interval notation):

A quadratic function is defined by f (x) = x + 5x 24. Which of the following expresses f (x) as the product of two linear factors? f (x) = (* - 4) (x + 6) A f (2) = (x - 3) (x + 8) f (x) = (x + 3) (x - 8) f (x) (x + 4) (x - 6)