At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To find [tex]\( g(f(x)) \)[/tex] for the given functions [tex]\( f(x) = x - 7 \)[/tex] and [tex]\( g(x) = 5x + 2 \)[/tex], we can follow these steps:
1. Find [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = x - 7 \][/tex]
2. Substitute [tex]\( f(x) \)[/tex] into [tex]\( g(x) \)[/tex] to find [tex]\( g(f(x)) \)[/tex]:
Because [tex]\( g(x) \)[/tex] is given by [tex]\( g(x) = 5x + 2 \)[/tex], we substitute [tex]\( f(x) \)[/tex] into [tex]\( g \)[/tex]:
[tex]\[ g(f(x)) = g(x - 7) \][/tex]
3. Apply the function [tex]\( g \)[/tex] to [tex]\( (x - 7) \)[/tex]:
Substitute [tex]\( (x - 7) \)[/tex] into the expression for [tex]\( g(x) \)[/tex]:
[tex]\[ g(x - 7) = 5(x - 7) + 2 \][/tex]
4. Simplify the expression:
[tex]\[ g(x - 7) = 5(x - 7) + 2 = 5x - 35 + 2 \][/tex]
[tex]\[ g(x - 7) = 5x - 33 \][/tex]
Thus, the function [tex]\( g(f(x)) \)[/tex] can be written in the form:
[tex]\[ g(f(x)) = 5x - 33 \][/tex]
From this expression, we see that the coefficient of [tex]\( x \)[/tex] is [tex]\( 5 \)[/tex] and the constant term is [tex]\( -33 \)[/tex]. Therefore:
[tex]\[ g(f(x)) = 5x + (-33) \][/tex]
So, the coefficients are:
[tex]\[ g(f(x)) = 5x + (-33) \][/tex]
The coefficient of [tex]\( x \)[/tex] is [tex]\( 5 \)[/tex].
The constant term is [tex]\( -33 \)[/tex].
Thus, the function [tex]\( g(f(x)) \)[/tex] can be expressed as:
[tex]\[ g(f(x)) = 5x - 33 \][/tex]
1. Find [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = x - 7 \][/tex]
2. Substitute [tex]\( f(x) \)[/tex] into [tex]\( g(x) \)[/tex] to find [tex]\( g(f(x)) \)[/tex]:
Because [tex]\( g(x) \)[/tex] is given by [tex]\( g(x) = 5x + 2 \)[/tex], we substitute [tex]\( f(x) \)[/tex] into [tex]\( g \)[/tex]:
[tex]\[ g(f(x)) = g(x - 7) \][/tex]
3. Apply the function [tex]\( g \)[/tex] to [tex]\( (x - 7) \)[/tex]:
Substitute [tex]\( (x - 7) \)[/tex] into the expression for [tex]\( g(x) \)[/tex]:
[tex]\[ g(x - 7) = 5(x - 7) + 2 \][/tex]
4. Simplify the expression:
[tex]\[ g(x - 7) = 5(x - 7) + 2 = 5x - 35 + 2 \][/tex]
[tex]\[ g(x - 7) = 5x - 33 \][/tex]
Thus, the function [tex]\( g(f(x)) \)[/tex] can be written in the form:
[tex]\[ g(f(x)) = 5x - 33 \][/tex]
From this expression, we see that the coefficient of [tex]\( x \)[/tex] is [tex]\( 5 \)[/tex] and the constant term is [tex]\( -33 \)[/tex]. Therefore:
[tex]\[ g(f(x)) = 5x + (-33) \][/tex]
So, the coefficients are:
[tex]\[ g(f(x)) = 5x + (-33) \][/tex]
The coefficient of [tex]\( x \)[/tex] is [tex]\( 5 \)[/tex].
The constant term is [tex]\( -33 \)[/tex].
Thus, the function [tex]\( g(f(x)) \)[/tex] can be expressed as:
[tex]\[ g(f(x)) = 5x - 33 \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.