newnaty1668 newnaty1668
  • 24-03-2022
  • Mathematics
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if f(x)=2^x and g(x)=x-4. The graph of (fog)(x) is shown below. What is the range of (fog)(x)?

if fx2x and gxx4 The graph of fogx is shown below What is the range of fogx class=

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goddessboi goddessboi
  • 24-03-2022

Answer:

C) [tex]y > 0[/tex]

Step-by-step explanation:

[tex]f(x)=2^x\\\\g(x)=x-4\\\\(f\circ g)(x)=f(g(x))=f(x-4)=2^{x-4}[/tex]

This means that the parent function, [tex]f(x)=2^x[/tex], will shift 4 units to the right along the x-axis, so this DOES NOT affect the range (nor the domain either). Thus,  [tex]y > 0[/tex] would be the range.

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