8) Given f(x) = 2x -1; g(x) = x² ;Calculate;a) f(3) b) g(-2)c) f(2d+1) d) f(g(2))O

We have given two functions fx=2x-1 gx=x2 (a) Put x=3 in f(x) f3=2×3-1 f3=6-1 f3=5 (b) Put x=-2 in…

Answered: 8) Given f(x) = 2x -1; g(x) = x² ;…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

8) Given f(x) = 2x -1; g(x) = x² ;
Calculate;
a) f(3) b) g(-2)
c) f(2d+1) d) f(g(2))
O

Expert Solution

Step 1

We have given two functions

$f (x) = 2 x - 1$

$g (x) = x^{2}$

(a) Put $x = 3$ in f(x)

$f (3) = 2 \times 3$ $- 1$

$f (3) = 6 - 1$

$f (3) = 5$

(b) Put $x = - 2$ in g(x)

$g (- 2) = {(- 2)}^{2}$

$g (- 2) = 4$

$f (2 d + 1) =$ $2 (2 d + 1) - 1$

$f (2 d + 1) = 4 d$ $+ 2 - 1$

$f (2 d + 1) = 4 d$ $+ 1$

(d) $f (g (2))$

Put x=2 in g(x)

$g (2) = 2^{2} = 4$

So,

$f (g (2)) =$ $f (4)$

Put x=4 in f(x)

$f (g (2)) =$ $2 \times 4 - 1$

$f (g (2)) = 8 - 1$

$f (g (2)) = 7$

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8) Given f(x) = 2x -1; g(x) = x² ; Calculate; a) f(3) b) g(-2) c) f(2d+1) d) f(g(2)) E3