If $f(x)=x^2-2x+4$, then the set of values of $x$ satisfying $f(x-1)=f(x+1)$ is

If $f(10-x)=3x^2+4x-5$ and $f(x)=px^2+qx+r$,then find the value of $p+q+r$.

If $f: R \rightarrow R$ is a differentiable function such that $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$ and if $f^{\prime}(4)=24$ and $f^{\prime}(0)=3$,then $f(4)=$

Let $f: R \rightarrow R$ be such that $f$ is injective and $f(x) f(y) = f(x+y)$ for $\forall x, y \in R$. If $f(x), f(y), f(z)$ are in $G$.$P$.,then $x, y, z$ are in:

Let $f\left( \frac{x + 8y}{9} \right) = \frac{f(x) + 8f(y)}{9}$ for all real $x$ and $y$. If $f'(0)$ exists and is equal to $2$,and $f(0) = -5$,then $f(7)$ is equal to:

If $f(a) = a^2 + a + 1$,then the number of solutions of the equation $f(a^2) = 3f(a)$ is: