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If [tex]f(x) = x^3 - 2x^2[/tex], which expression is equivalent to [tex]f(t)[/tex]?

A. [tex]-2 + i[/tex]
B. [tex]-2 - i[/tex]
C. [tex]2 + i[/tex]
D. [tex]2 - i[/tex]

Sagot :

GinnyAnsweridn
To find the expression equivalent to [tex]\( f(t) \)[/tex] given that [tex]\( f(x) = x^3 - 2x^2 \)[/tex], we simply need to substitute [tex]\( t \)[/tex] in place of [tex]\( x \)[/tex] in the function [tex]\( f(x) \)[/tex].

Given:
[tex]\( f(x) = x^3 - 2x^2 \)[/tex]

Substituting [tex]\( t \)[/tex] for [tex]\( x \)[/tex]:
[tex]\[ f(t) = t^3 - 2t^2 \][/tex]

Hence, the expression equivalent to [tex]\( f(t) \)[/tex] is:
[tex]\[ t^3 - 2t^2 \][/tex]

None of the provided answer choices [tex]\(-2+i\)[/tex], [tex]\(-2-i\)[/tex], [tex]\(2+i\)[/tex], or [tex]\(2-i\)[/tex] are equivalent to [tex]\( t^3 - 2t^2 \)[/tex].

Thus, the expression equivalent to [tex]\( f(t) \)[/tex] is:
[tex]\[ t^3 - 2t^2 \][/tex]
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