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Solution

Given f(x)=2x^2+7

Need to find f(x+3)-[f(x)+3].

f(x+3) is obtained by substituting x+3 in place of x in f(x)

So,f(x)=2x^2+7

f(x+3) = 2(x+3)²+7

= 2(x²+3²+2(x)(3))+7

= 2(x²+9+6x)+7

= 2x²+12x+18+7

= 2x²+12x+25

f(x)+3 can be obtained by adding 3 to the function f(x)

So,[f(x)+3] = [(2x²+7)+3]

= 2x²+7+3

= 2x²+10

f(x+3)-[f(x)+3] = 2x²+12x+25 - ( 2x²+10)

= 2x²+12x+25-2x²-10

= 12x+15

Therefore, f(x+3)-[f(x)+3] = 12x+15