Concept explainers
Finding a Pattern Consider the function
(a) Use the Product Rule to generate rules for finding
(b) Use the results of part (a) to write a general rule for
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Calculus of a Single Variable
- find : (f+g)(x) (f-g)(x) (f•g)(x) (f/g)(x) and their domainsarrow_forwardx + 9 If f(x) = 6x 9 and g(x) = (a) f(g(x)) = (b) g(f(x)) = (c) Thus g(x) is called an function of f(x)arrow_forwardX Find the following for the function f(x) 2 X +1 (a) f(0) (e) - f(x) (b) f(8) (f) f(x + 3) (c) f( - 8) (g) f(4x) (d) f(- x) (h) f(x + h)arrow_forward
- f (h+4)-f (4) (***) Use the function f (x)=3x² – 5x to evaluatearrow_forwardfind the function of f(2) and f(3)arrow_forwardSuppose that for some function f that f(x + 2) = 7x (a) Explain why f(2) = 0 (b) Explain why f(3) = 7 (c) Evaluate f(4) (d) Evaluate f(5) (e) Evaluate f(6) (f) Find the equation for f(x)arrow_forward
- x + 8 If f(x) = 4x – 8 and g(x) 4 (a) f(g(x)) Preview (b) g(f(x)) : Preview (c) Thus g(x) is called an function of f(x)arrow_forwardI +9 If f(x) = 7x 9 and g(x) 7 (a) f(9(x)) = (b) g(f(x)) = (c) Thus g(x) is called an function of f(x)arrow_forwardx + 7 If f(x) = 4x – 7 and g(x) 4 (a) f(g(x)) = (b) g(f(x)) = (c) Thus g(x) is called an function of f(x)arrow_forward
- (a) first find f+g, f-g, fg, and f/g. Then determine the domain for each function f(x)=5x-1, g(x)=x-5 (b) given f(x)=5x+9 and g(x)=3x^2, first find f+g, g-f, fg. and f/g. Then determine the domain for each functionarrow_forwardFind the functions (a) (f∘g)(x)(f∘g)(x), and (b) (g∘f)(x)(g∘f)(x) and their domains. f(x) = x-2 g(x)= x^2 + 3x +4arrow_forward4 The functions f and g are defined as f(x) = X+2 9(x) = 7-x a) Find the domain of f, g, f+ g, f-g, fg, ff, and f b) Find (f+ g)(x), (f– g)(x), (fg)(x). (ff)(x), -|x (x), and (x). a) The domain of f is (Type your answer in interval notation.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage