If f(x)=2x+1 and g(x)=x^2-3, find EACH of the following : a)f(g(1))= b)g o f(-3)

Question

If f(x)=2x+1 and g(x)=x^2-3, find EACH of the following :

a)f(g(1))=

b)g o f(-3)=

c)f(g(x)=

d)g(f(x)=

e)f(g(2a))=

f)g(f(2a+1)

2)Explain the EFFECT on the graph of g(x)=sinx after it is compsed with f(x) to form f(g(x)) in Each of the following:

a)f(x)=x+2

b)f(x)=-2x

c)f(x)=2x+4

3)Flourine-20 is a radioactive substance that decays over time.At time 0, the mass of a sample of the substance is 20 g. The mass decreases to 10g after 11 s, to 5 g after 22 s, and to 2.5 g after 33 s. COMPARE the AVERAGE rate of change over the 33 s interval with the AVERAGE rate of chnage over consecutive 11-s intervals.

4)Explain why there are NO solutions to the equations log (base 5)-125=x and log 9base -2)16=x?

Explanation / Answer

1.(a) g(1) = 1^2 - 3 = 1 - 3 = -2

f(-2) = 2*(-2) + 1 = -4 + 1 = -3

Hence f(g(1)) = -3

(b) f(-3) = 2*(-3) + 1 = -6 + 1 = -5

g(-5) = (-5)^2 - 3 = 25 - 3 = 22

g o f(-3) = g(f(-3)) = 22

(c) f(g(x)) = f(x^2 - 3) = 2*(x^2 - 3) + 1 = 2x2 - 6 + 1 = 2x2 - 5

(d) g(f(x)) = g(2x + 1) = (2x+1)2 - 3 = 4x2 + 4x + 1 - 3 = 4x2 + 4x - 2

(e) f(g(2a)) = 2(2a)2 - 5 = 8a2 - 5

(f) g(f(2a+1)) = 4(2a+1)2 + 4(2a+1) - 2 = 16a2 + 16a + 4 + 8a + 4 - 2 = 16a2 + 24a + 6

2. g(x) = sin x

(a) f(x) = x +2

f(g(x)) = sin x + 2

Graph moves up by 2 units.

(b) f(x) = -2x

f(g(x)) = -2sin x

Graph becomes inverted and magnifies as twice as the original.

(c) f(x) = 2x + 4

f(g(x)) = 2sin x + 4

Graph magnifies as twice as the original and moves up by 4 units.

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