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7. [1/2 Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the functions $f(x) = 2x + 5$ and $g(x) = 3x^2$ to calculate each operation and simplify, if possible. Enter DNE if the operation cannot be computed. (a) $(f\circ g)(x) = 6x^2+5$ (b) $(g\circ g)(x) = 5x^2+5$ Submit Answer

          7. [1/2 Points]
DETAILS
PREVIOUS ANSWERS
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Use the functions $f(x) = 2x + 5$ and $g(x) = 3x^2$ to calculate each operation and simplify, if possible. Enter DNE if the operation cannot be computed.
(a) $(f\circ g)(x) = 6x^2+5$
(b) $(g\circ g)(x) = 5x^2+5$
Submit Answer
        
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7. [1/2 Points]
DETAILS
PREVIOUS ANSWERS
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Use the functions f(x) = 2x + 5 and g(x) = 3x^2 to calculate each operation and simplify, if possible. Enter DNE if the operation cannot be computed.
(a) (f∘ g)(x) = 6x^2+5
(b) (g∘ g)(x) = 5x^2+5
Submit Answer

Added by Janice C.

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Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Alan S. Tussy, R. David Gustafson 5th Edition
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Use the functions f(x) = 2x + 5 and g(x) = 3x^2 to calculate each operation and simplify, if possible. Enter DNE if the operation cannot be computed. a) f(6) + g(6) b) f(6) - g(6) c) f(6) * g(6) d) f(6) / g(6)
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Transcript

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00:01 Okay, we're looking at the functions f of x equals 1 over x minus 6 and g of x equals 7 over x plus 6.
00:06 So we know that f of g of x is going to be f of 7 over x plus 6, which is going to be the same thing as 1 over 7 over x plus 6 minus 6, which is going to be equivalent to 1 over 7 over x.
00:28 Obviously, this is because 6 minus 6 is just 0.
00:32 Now we know this is the same thing as x over 7.
00:36 However, we know that x does not equal 0 because we know the domain of g is going to be negative.
00:45 And so the domain of g is going to be negative infinity, comma 0, 0, infinity...
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