f(x)=2x^2+3; g(x) =4x^3 +1

 

(a) (f + g)(x)

(b) (f - g)(x)        (c) (f . g)(x)   

(g) (f . g)(2)         (d) (f/g) (x)

(h) (f/g) (1)          (e) (f + g)(3)

(f) (f - g)(4)

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1 Answer

(a) 2x^2+3 + 4x^3+1=4x^3+2x^2+4 (simply add the definitions of the two separate functions)

(b) -4x^3+2x^2+2

(c) multiply: (2x^2+3)(4x^3+1)=8x^5+12x^3+2x^2+3

(d) divide: (2x^2+3)/(4x^3+1) has a domain that excludes 4x^3+1=0, 4x^3=-1 so x=-cuberoot of (1/4) is excluded from the domain. All other real values of x are permitted.

The domains of (a) - (c) put no constraints on x, so the domain is the real numbers.

(e) put x=3 in (a): 4*27+2*9+4=130

(f) put x=4 in (b): -4*64+2*16+2=-222

(g) put x=2 in (c): 8*32+12*8+2*4+3=363

(h) put x=1 in (d): 5/5=1

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