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Question 12 of 23 (1 point) Find two functions f and g such that h(x)=(fog)(x) and f(x) * g() + x. n(x) = */7x +5 f(x)=0 and g(x)=0 Question 14 of 23 (1 point) The one-to-one function is given. Write an equation for the inverse function. 2 s(x) = х 3
5. Let f R2 ->R2 be the function given by f(x, y) (х + у, х — у). (i) Prove that f is linear as a function from R2 to R2. (ii) Calculatee the matrix of f. (iii) Prove that f is a one-to-one function whose range is R2. Deduce that f has an inverse function and calculate it. (iv) If C is the square in R2 given by C = [0,1] x [0, 1], find the set f(C), illustrating...
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)
a. 4. Let h(x) = x4 – 6x3 + 12x2. Find h'(x) and h"(x). b. Find the open intervals on which h is concave upward and concave downward. Give the points of inflection for h as ordered pairs. c. a. 5. Let g(x) = x4 – 2x3 + 3. x3 This function is defined, differentiable, for all real numbers except x = where g has a vertical asymptote. b. Find g'(x), given any other value of x. c. Suppose we...
Find fog and go f. f(x) = x5, g(x) = x (a) fog 1.25 х (b) gof 1.25 X Find the domain of each function and each composite function. domain off domain of g domain of fog domain of g of
2) (12) f:R-(3/2)-R-10, (x) 1/(3 2x) g:R--21->R-1o), g (x)1/ (x 2) h:R-(-4/3]-R-(1/3), h(x) (f o g) (x) Verify if h(x) is one to one and onto. If it is, find the inverse function of h(x). 2) (12) f:R-(3/2)-R-10, (x) 1/(3 2x) g:R--21->R-1o), g (x)1/ (x 2) h:R-(-4/3]-R-(1/3), h(x) (f o g) (x) Verify if h(x) is one to one and onto. If it is, find the inverse function of h(x).
f(x+h)-f() Find the difference quotient h where h# 0, for the function below. F f(x) = 2x² + 2x Simplify your answer as much as possible. h G х ?
Question 2 Find the indicated function value. Find f(-4) when f (x) 2² +4 23 62 O-2/7 0-5/16 0 - 1/2 O-2/5 Question 3 BILI SUULILULUI NV, O Question 5 3 pts Find the indicated function value: f(3) = 5 - 8a, g(x) = -3x + 8. Find (f + 9) (x) - 3x + 5 - 5x + 13 0 - 11x + 13 2x Question 6 3 pts Find the composition of functions: f(x) 70? + 4x, g(x)...
f(x +h)-f(x) Find the difference quotient off; that is, find h h#0, for the following function. Be sure to simplify. f(x) = x2 - 8x+2 f(x +h)-f(x) h (Simplify your answer.)
Question 1 The functions f(x) g(x) and h(x) are defined as follows: f(x) = e* XER g(x) = x x 20 h(x) = 2x + 1 XER [3 marks] Find fg(x) and state its domain and range Find hf (x) and state its domain and range Find hº(x) and state its domain and range __[3 marks] (1111) [3 marks] WA (b) The figure below shows the graph of y=-x-shifted to four new positions. Write an equation for each new graph....