Given f : R → R defined by f(x) = x · e x and g : R → R defined by g(x) = √x² + 1.
(a) Find f ο g
(b) Find g ο f
(c) Find the range of g and state the range of g in correct set notation
(d) Let S = (−1, 1) = {x ∈ R | − 1 < x < 1}. Find g(S) and express g(S) in correct set notation.
(e) Let T = {√2}. Find g⁻¹ (T) and express g⁻¹ (T) in correct set notation.

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b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation:

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.

step-by-step explanation: