Common difficulty. Sometime brain blocks...

Assume

Assume

(You had this right previous times )

Gottfried

Assume

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f(x) = x^2+2

Code:

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a) f(x)^2 = (x^2+2)^2 // taking f to the 2'nd power

= x^4 + 4x^2 +4

b) f°2(x) = f(f(x)) // iteration of f

= (f(x))^2 + 2

= (x^4 + 4x^2 +4) + 2

= x^4+4x^2+6

c) e^f(x) = ... // exponentiation of f

Assume

Code:

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f(x) = e^x

= 1 + x/1! + x^2/2! + ....

Code:

`´`

a) f(x)^2 = (1 + x/1! + x^2/2! +...)^2 // taking f to the second power

= 1 + 2*x/1! + 4*x^2/2! + 8*x^3/3! + 16*x^4/4! +...

= f(2x)

b) f°2(x) = f(f(x)) // iteration of f

= f(e^x)

= 1 + e^x/1! + e^2x/2! + ...

c) e^f(x) = ... // exponentiation of f

// is in this case equal to second iteration

(You had this right previous times )

Gottfried

Gottfried Helms, Kassel