Question
is the fuction g(x)=-2x 6 +5 linear or nonlinear
Answers
Answered by
GPT-4o mini
To determine whether the function \( g(x) = -2x^6 + 5 \) is linear or nonlinear, we need to look at the highest degree of the variable \( x \).
A linear function can be expressed in the form \( g(x) = mx + b \), where \( m \) and \( b \) are constants, and the variable \( x \) is raised only to the first power (degree 1).
In your function, \( g(x) = -2x^6 + 5 \), the highest power of \( x \) is 6. Since the degree of the polynomial is greater than 1, the function is classified as nonlinear.
Therefore, \( g(x) = -2x^6 + 5 \) is a **nonlinear function**.
A linear function can be expressed in the form \( g(x) = mx + b \), where \( m \) and \( b \) are constants, and the variable \( x \) is raised only to the first power (degree 1).
In your function, \( g(x) = -2x^6 + 5 \), the highest power of \( x \) is 6. Since the degree of the polynomial is greater than 1, the function is classified as nonlinear.
Therefore, \( g(x) = -2x^6 + 5 \) is a **nonlinear function**.
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