turkey-yks 2012 Q42

turkey-yks · Other · lys1-math Composite & Inverse Functions Derivative of an Inverse Function

For functions f and g defined on the set of real numbers
$$\begin{aligned} & f ( g ( x ) ) = x ^ { 2 } + 4 x - 1 \\ & g ( x ) = x + a \\ & f ^ { \prime } ( 0 ) = 1 \end{aligned}$$
Given this, what is a?
A) $-2$
B) $\frac { -1 } { 4 }$
C) 1
D) $\frac { 3 } { 2 }$
E) 3

For functions f and g defined on the set of real numbers

$$\begin{aligned}
& f ( g ( x ) ) = x ^ { 2 } + 4 x - 1 \\
& g ( x ) = x + a \\
& f ^ { \prime } ( 0 ) = 1
\end{aligned}$$

Given this, what is a?

A) $-2$\\
B) $\frac { -1 } { 4 }$\\
C) 1\\
D) $\frac { 3 } { 2 }$\\
E) 3

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