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Question 10 Define the function $f: \mathbb{R} \rightarrow \mathbb{R}$ as follows: For every real number $x$, $f(x) = \frac{2x - 1}{x + 1}$. (1) The domain of $f$ is [Select] (2) Is the function $f$ onto? [Select] (3) Is the function $f$ one-to-one? [Select] 6 pts

          Question 10
Define the function $f: \mathbb{R} \rightarrow \mathbb{R}$ as follows: For every real number $x$,
$f(x) = \frac{2x - 1}{x + 1}$.
(1) The domain of $f$ is [Select]
(2) Is the function $f$ onto? [Select]
(3) Is the function $f$ one-to-one? [Select]
6 pts
        
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Question 10
Define the function f: ℝ→ℝ as follows: For every real number x,
f(x) = (2x - 1)/(x + 1).
(1) The domain of f is [Select]
(2) Is the function f onto? [Select]
(3) Is the function f one-to-one? [Select]
6 pts

Added by Olivia J.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Question 10 6 pts Define the function f : R > IR as follows: For every real number 2x -1 f(x)= +1 (1) The domain of f is [Select] (2) Is the function f onto? [Select] (3) Is the function f one-to-one? [Select]
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Transcript

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00:01 So in this problem, we are giving for problem number three, just to start off with, we're given that f of x is equal to x to the third powered.
00:12 So for the first part, part one, let's call it a.
00:17 F of zero is just going to be zero to the third powered, which is zero.
00:22 For part b, f of negative 2 would be negative 2 to the third powered, which is negative 8.
00:28 For part c, we are supposed to find the value of the function at 2.
00:33 So f of 2 is going to equal 2 to the 3rd powered, which is 8.
00:39 And for part d, we're supposed to simplify f of x plus delta x minus f of x divided by delta x, which will equal to x plus delta x to the third power minus x of the third powered, divided by delta x.
01:00 So this is going to equal to the x plus delta x to the third power.
01:03 We have to expand that.
01:05 And let's see.
01:07 That's going to be x to the third power to begin with plus 3x times, so 3x squared times delta x, plus 3x times delta x squared plus delta x to the third power minus x of the third power...
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