1. The problem statement, all variables and given/known dataLet F be the vector space of all functions mapping R into R and let T: F -> F be a linear transformation such that T(e^2x) = x^2, T(e^3x) = sinx, and T(1) = cos5x. Find the following, if it is determined by the data. a. T(e^5x) b. T(3e^4x) c. T(3 + 5e^3x) c. T((e^4x + 2e^5x)/e^2x) 2. Relevant equationsNone 3. The attempt at a solutionI know that a linear transformation preserves vector addition and scalar multiplication. To get e^5x, I need to multiply e^2x and e^3x. Would this be scalar multiplication? I figured it would not be because they are vectors in this circumstance. The other problems are similar. Can I multiply them? if so, why?