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Use the given information to find f '(2). g(2) = 3 and g'(2) = -3 h(2)...
Given f(x), find g(x) and h(x) such that f(x)=g(h(x)) and neither g(x) nor h(x) is solely x. f(x)=3√(5x^2+4)+1 g(x)= h(x)=
1 2) (15 pts) Given g(x) g(x+h)-g(x) use the formula g'(x) = lim 6x+3' h0 h to find g'(x). 3) (15 pts) Given h(x) = -3x2 + 5x + 2, find the equation of the tangent line at x = -2. (Hint: For the tangent line at x = a, find f(a), and f'(a).)
For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. f(x) = x – 6; g(x) = 6x? What is the domain of -? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain is {x|}. (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is {x| x is any...
8. Suppose that we are given the following information about the functions f, g, h and k and their derivatives; • f(1) = 3 • f'(1) = 2 • g(1) = 4 • g'(1) = -2 • h(1) = 9 . h'(1) = -1 k(1) = 10 • k'(1) = -3 (e) (5 points) Set F(x) = log2[f(x) + g(x)]. Compute F'(1). (f) (5 points) Set F(T) = log: [f(r)g(r)h(r)k(r)]. Compute F'(1).
Given f(x) = 2x + 3 and g(x) = x^2 Find f(x) + g(x) f(x) - g(x) f(x) · g(x) f(x) / g(x) f(g(x)) g(f(x)) Given f(x) = x^2 + 2x -1 and g(x) = 3x Evaluate f(2) g(9) f(g(4) g(f(4))
g(x) = 2x -1, 8)) Given f(x) = x?, a) f(g(x)) h(x) = Vx+2; find the following: b) g(h(x))
(1 point) Use the given functions to evaluate the statements. f(g(-2))= (f.g)(3) = f(g(-3)) = 3 2 -2 -1 1 -3 -4 X 31 -4 -1 f(x) -2 0 4 -3 2 е(к)
For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. 3x +7 f(x) = 7x-3 9(x) = 6x 7x-3 (a) Find (f+g)(x). (*+g)(x)=(Simplify your answer.) What is the domain off+g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain is {x}. (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B....
Q4 (4 points) (a) (1.5p) Find f +g-h, fog, fog•h if f(x) = (x - 3, g(x) = x^, and h(x) = x* + 2 (b) 0(1p) Find the inverse of the function f(x) = 4x - 1 2x + 3 () (0.5p) Find f(-)) (c) Simplify: 0 (1p) In(a) + { ln(b) + Inc mais)
Suppose that f(2) = -3, 9(2) = 4, f'(2) = -5, and g(2) = 1. Find h'(2). (a) h(x) = 3f(x) - 2g(x) h'(2) h(x) = f(x)g(x) (b) h'(2) (c) h(x) = f(x) g(x) h'(2) (d) h(x) g(x) 1 + f(x) h'(2)